# What is Confounding in a 2k Factorial Design

Let’s expand the 22 basic factorial design to a 23 design for three variables in Table 3. Eight experimental units will be required to complete a full replication of the 23 design. However, if only four samples or experimental units can be produced from one batch, there are not enough samples or experimental units to complete the full replication of the 23 factorial design. Therefore, two batches/blocks are required to complete the full replication of the 23 factorial design. Therefore, one (2-1 = 1) degrees of freedom is lost due to the two blocks. One effect won’t be possible to estimate from this experiment. Generally, higher-order interaction terms are practically meaningless. Therefore, the higher-order interactions are sacrificed when there are not enough experimental units are available. For an example, in a 23-factorial design of experiment, the three-way interaction (ABC interaction) is sacrificed by confounding with the block, meaning that it won’t be possible to distinguish the effect of ABC interaction from the block effect. To make the ABC interaction indistinguishable from the block, all the “positive terms” and the “negative terms” in the contrast of ABC is run in separate blocks. The indistinguishable effects are known as confounded effects. Of course, the run orders are selected randomly within the block, rather than the standard order, as in any other experimental designs. The entire systematic process of making some effects indistinguishable by blocking is known as confounding.

Table 3. The 23 Factorial Design of Experiments